Sounds like a Moen Posi-temp control. Since the hot can only be achieved by moving the handle thru the cold over to the hot, it's impossible you have a handle or 'stop" adjustrment problem. And since you can shut off the water, it means your handle is not lose or broken.
I am not sure how this may be causing this. But I'm thinking that the slide pin inside that keeps the temperature even, in case someone turned hot or cold water in the house, got stuck inside the cartridge. You can remove the cartridge and maybe get another one for free. Maybe. Some places are more strict about if you were the original owner and were the one who installed. Other places do not really care and give you one. You could also call up Moen and they may send you one if you run into problems this way.
It is possible that it is not cartridge related also, especailly if your house was old with galvanized pipes, OR, if say the city turned off your water and when they turned it back on, junk came through your water pipes and got hung up either in the cartridge of mixer. I am not about to go into a detailed post again about how to flush the line. I did that today once already on another post. Maybe someone else can help out here, if need be.
To remove your cartridge:
TURN OFF THE WATER TO THE HOUSE. Then maybe flush a toilet to release presure.
Be prepared when removing parts that you set aside an area to lay parts out in order of removal and orientation!!!
You have to unscrew the handle. The handle may be held on by screw hiding under a cover plate on the handle or by some set screw.
Once you get off the handle, you pull off 2 white plastic things that have gear teeth on them. Be careful with these so that you are able to put them back in in exactly as how you removed them!
Now you will be able to pull off this chrome 1 1/4? inch tube.
Hiding under this tube, that has a raised length-running square ontop, you will find out why it has that raised square: There is a brass fork piece that is slid down thru from the top, through the 1 1/4? inch brass body of the mixer. You can grab that fork with say a needlenose pliers, and pull it out of the slot.
With that out, now the cartridge will pull out. Sometimes they are stuck in there pretty well, and you can't even hardly pull them out, even if you latch onto the stem with a vicegrips and put your foot against the tub and yank! - they can be stuck THAT bad. So, what the company does is include in the cartridge package a little plastic square tool, that helps you get out the cartridge. You slip that tool over the stem and up against the valve body and hold it there tight while you use a crescent wrench or channel locks and TURN that white square. What that does is force the cartridge to turn, breaking it's frozen bond. The side of the valve body is ramped so that as the cartridge turns, it also squirts out maybe 1/8th inch. NOW you can yank it out with a vice grips. Carefully observe any markings or wording on this cartridge so your new one goes in the same way.
Then put in new free cartridge (it may say hot and cold on the white plastic of the cartridge, so orient it correctly with hot on the left -and put on everything in reverse order. There will also be a small little metal washer on the stem. Remove it to use on the new cartridge. This washer is a stop for the handle. Also, you will not get that fork back in the slot unless you have the cartridge perfectly vertical, and if you can't get the fork to drop in, you have to sometimes fiddle with turning the cartridge slightly to get it to go all the way down. You must make sure the bottom of the fork passes into the bottom of the valve body to lock it in.
(I have done tons of these things over the years,)
